Synthesis of Boundary Conditions in Polygonal Magnetic Domains Using Deep Neural Networks

Sami Barmada (), Paolo Di Barba and Maria Evelina Mognaschi
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Sami Barmada: Department of Energy, Systems, Territory and Construction Engineering, University of Pisa, 56126 Pisa, Italy 2 Department of Electrical, Computer and Biomedical Engineering, University of Pavia, 27100 Pavia, Italy
Paolo Di Barba: Department of Electrical, Computer and Biomedical Engineering, University of Pavia, 27100 Pavia, Italy
Maria Evelina Mognaschi: Department of Electrical, Computer and Biomedical Engineering, University of Pavia, 27100 Pavia, Italy

Mathematics, 2024, vol. 12, issue 23, 1-17

Abstract: In this paper, the authors approach the problem of boundary condition synthesis (also defined as field continuation) in a doubly connected domain by the use of a Neural Network-based approach. In this innovative method, given a field problem (magnetostatic, in the test case shown here), a set of Finite Element Method simulations is performed in order to define the training set (in terms of the potential over a domain) by solving the direct problem; subsequently, the Neural Network is trained to perform the boundary condition synthesis. The performances of different Neural Networks are compared, showing the accuracy and computational efficiency of the method. Moreover, domains externally bounded by two different kinds of polygonal contours (L-shaped and three-segments, respectively) are considered. As for the latter, the effect of the concavity/convexity of the boundary is deeply investigated. To sum up, a classical field continuation problem turns out to be revisited and solved with an innovative approach, based on deep learning.

Keywords: field continuation problem; deep learning; magnetic field (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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